Omnidirectional LED light bulb
Summary by NHIP
Omnidirectional LED bulb with dual lenses
The bulb uses two LEDs facing different directions, each paired with a lens to redistribute light. Each lens creates a distribution with less than 0.53 average absolute value deviation from a normalized mean intensity of 1.0 within a 2π steradian solid angle.
Claim Score by NHIP
Abstract
An LED light bulb has a hollow LED support/heat sink (222, 602, 702, 900, 802, 1002, 1102, 1216, 1404, 1502, 1606, 1906) with fins (234, 406, 604, 706, 804, 904, 906, 1008, 1106, 1620) extending internally and openings at two ends (230, 232, 1522). Heat generated by the LEDs (238, 908, 1242, 1624, 2504) is conducted through the heat sink fins and is removed by a convectively driven air flow that flows through the LED support/heat sink. LEDs are mounted on multiple external faces (236, 404, 910, 1524, 1622) of the LED support/heat sink thereby providing illumination in all directions. Lenses (1246, 2102, 2104) are provided for the LEDs to make the illumination highly uniform.
Term
Projected expiry 15 January 2029.
- Priority
- Filed
- Granted
- Today
- Projected expiry
23 claims: 2 independent, 21 dependent
- 1Broadest claimClaim Score 49, average(NHIP)An omnidirectional LED light bulb comprising:a first LED oriented to face a first direction;a second LED oriented to face a second direction;a first lens optically coupled to said first LED;a second lens optically coupled to said second LED;wherein said first lens comprises at least one surface shaped to redirect light from said first LED so as to redistribute said light from said first LED to produce a light distribution that has a first average absolute value deviation of less than 0.53 from a normalized mean intensity of 1.0 within a first solid angle of 2π steradian;wherein said second lens comprises at least one surface shaped to redirect light from said second LED so as to redistribute said light from said second LED to produce a light distribution that has a second average absolute value deviation of less than 0.53 from a normalized mean intensity of 1.0 within a second solid angle of 2π steradian.
- 23An omnidirectional LED light bulb comprising:a first LED facing in a first direction;a second LED mounted facing in a second direction;a first lens optically coupled to said first LED and a second lens optically coupled to said second LED;a diffuser disposed around said first LED and said second LED so as to intercept light transmitted by said first lens and said second lens;wherein said first lens and said second lens each comprise at least one surface shaped to redistribute light from said first LED and said second LED so as to reduce light intensity along respective optical axes of said first LED and said second LED and to reduce light intensity in a polar angle range below a predetermined polar angle defined with respect to optical axes of said first LED and said second LED and serve to increase light intensity in a polar angle range above said predetermined angle;and wherein at least said diffuser, said first lens and said second lens serve to create a light distribution that is substantially azimuthally uniform with respect to an azimuth angle defined about a longitudinal axis of said omnidirectional LED light bulb.
Independent claims2
111 paragraphs in 5 sections, as filed
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a National Stage Application of PCT International Application No. PCT/US2009000244 filed Jan. 15, 2009 which is based on U.S. Provisional Patent Application 61/011,180 filed Jan. 15, 2008.
FIELD OF THE INVENTION
The present invention relates to general illumination with Light Emitting Diodes.
BACKGROUND OF THE INVENTION
Traditionally Light Emitting Diodes (LEDs) have primarily been used as indicator lamps in electronic equipment. However recently the power and efficacy (e.g., lumens per watt of electrical power) has been increasing and LEDs have been identified as a possible replacement for inefficient incandescent bulbs.
Like incandescent light bulbs, LEDs generate a certain amount of heat. Whereas incandescent light bulbs radiate a large amount of heat as infrared radiation in the case of LEDs heat must mainly be dissipated by conduction and convection. It is important to prevent the temperature of LEDs from rising too much because as the temperature of the LED increases its light output, efficacy and lifetime decrease. Thus, the promised benefits of LED lighting in terms of efficacy and lifetime can be diminished. A single power LED produces several tens of lumens, so in order to match the light output of an incandescent light bulb ten or more LEDs would typically be required. More LEDs mean a greater heat load.
<figref idrefs="DRAWINGS">FIG. 1</figref> shows a prior art LED light bulb <b>100</b>. A set of four rectangular circuit boards <b>102</b> (two of which are visible) are arranged in a box formation. A smaller square circuit board <b>104</b> is arranged to close a top end of the box formation. LEDs <b>106</b> are mounted on the circuit boards <b>102</b>, <b>104</b>. The arrangement of circuit boards <b>102</b>, <b>104</b> is enclosed in a space formed between a bulb shaped cover <b>108</b> and a lower plastic housing <b>110</b>.
From a thermal standpoint, this arrangement tends to trap heat within the enclosed space leading to a relatively limited power handling capacity of such bulbs. At such low powers as can be used with this design, the light produced is inadequate to match a conventional incandescent lamp or a compact fluorescent lamp.
From an optical point of view, the light distribution is best described as ad hoc. The LEDs used may be Lambertian emitters or more directional than that so that the LEDs on the rectangular circuit boards <b>102</b> provide illumination that is highly peaked along the direction perpendicular to the boards <b>102</b> surfaces and likewise the LEDs on the smaller square top board <b>104</b> provide illumination that is highly peak in the upward direction. Generally there is no expectation or realization of illumination patterns that blend together to provide anything approaching uniform illumination. Thus, optically this bulb inadequately matches the light distribution of standard incandescent bulbs.
BRIEF DESCRIPTION OF THE FIGURES
The present invention will be described by way of exemplary embodiments, but not limitations, illustrated in the accompanying drawings in which like references denote similar elements, and in which:
<figref idrefs="DRAWINGS">FIG. 1</figref> shows a typical prior art LED light bulb;
<figref idrefs="DRAWINGS">FIG. 2</figref> is an exploded view of an LED light bulb according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 3</figref> is a view of the LED light bulb shown in <figref idrefs="DRAWINGS">FIG. 2</figref> assembled;
<figref idrefs="DRAWINGS">FIG. 4</figref> is an end view of an extruded segment of an LED support/heat sink according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 5</figref> shows four segments of an LED support/heat sink that is made up of multiple segments;
<figref idrefs="DRAWINGS">FIG. 6</figref> shows an LED support/heat sink segment with cross-cut extruded fins according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 7</figref> shows an LED support/heat sink segment with a folded fin and an associated X-shaped brace according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 8</figref> shows an LED support/heat sink with pin fins according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 9</figref> shows an end view LED support/heat sink segment with a branched heat sink fin according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 10</figref> shows an LED support/heat sink segment with stacked fins according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 11</figref> shows an LED support/heat sink segment that includes a stack of fins bent at different angles according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 12</figref> is an exploded view of an LED bulb according to an alternative embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 13</figref> shows a partial sectional view of the bulb shown in <figref idrefs="DRAWINGS">FIG. 12</figref>;
<figref idrefs="DRAWINGS">FIG. 14</figref> is a partially exploded view of an LED light bulb according to an alternative embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 15</figref> is a partial X-ray view of an LED light bulb according to a further embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 16</figref> is perspective view of an LED light bulb according to a still further embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 17</figref> shows a bulb shape cover that includes phosphor particles according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 18</figref> is a magnified view of a portion of the bulb shaped cover shown in <figref idrefs="DRAWINGS">FIG. 18</figref>;
<figref idrefs="DRAWINGS">FIG. 19</figref> shows an omnidirectional LED bulb that includes a fan (or alternatively another active air moving device) for forced convection cooling according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 20</figref> is a plot of a generatrix of a surface of a primary lens for use in an omnidirectional LED light bulbs according to an embodiment of the invention;
<figref idrefs="DRAWINGS">FIG. 21</figref> is a graph including plots of generatrices of surfaces of a secondary lens that can be used to obtain more uniform illumination from white LEDs that are approximately Lambertian emitters;
<figref idrefs="DRAWINGS">FIG. 22</figref> is a graph showing the radiant light intensity versus polar angle for an LED that produces a quasi-Lambertian light distribution as a series of measured data points along with a plot of the Lambertian distribution;
<figref idrefs="DRAWINGS">FIG. 23</figref> is a graph of radiant light intensity versus polar angle produced using an LED having the distribution shown in <figref idrefs="DRAWINGS">FIG. 22</figref> in combination with a lens of the type shown in <figref idrefs="DRAWINGS">FIG. 21</figref>.
<figref idrefs="DRAWINGS">FIG. 24</figref> schematically illustrates the geometry of the LED support/heatsinks used in the omnidirectional LED bulbs in a coordinate system;
<figref idrefs="DRAWINGS">FIG. 25</figref> shows an end view of the LED support/heatsink with a schematic illustration of the manner in which the solid angle about the omnidirectional bulbs is illuminated.
DETAILED DESCRIPTION
<figref idrefs="DRAWINGS">FIG. 2</figref> is an exploded view of an LED light bulb <b>200</b> according to an embodiment of the invention. Referring to <figref idrefs="DRAWINGS">FIG. 2</figref> a lower assembly <b>202</b> includes an Edison type base <b>204</b> coupled to a housing <b>206</b>. (Alternatively, a terminal base other than Edison style is used.) A printed circuit board <b>208</b> is located is located in the housing <b>206</b>. Alternatively more than one smaller circuit board is used. The printed circuit board <b>208</b> is connected to the Edison style base <b>204</b> by a pair wires <b>210</b>. The printed circuit board <b>208</b> includes a circuit for adapting power received through the Edison style base <b>204</b> for driving LEDs. The circuit suitably comprise a switch mode buck power supply for converting relatively high household AC voltage to a lower DC voltage. Alternatively, in the case that LEDs that operate on household AC power are used, it is possible to eliminate the circuit board <b>208</b>. The lower assembly is shown in partial X-ray view so that the internal structure can be seen.
A vertically (in the perspective of <figref idrefs="DRAWINGS">FIG. 2</figref>) extending stem <b>212</b> is received in a cylindrical recess <b>214</b> at the top of the housing <b>206</b>. The vertically extending stem <b>212</b> is coupled to and supports an “X” shaped brace <b>216</b>. The vertically extending stem <b>212</b> fits into a central bore <b>218</b> of “X” shaped brace <b>216</b>. The “X” shaped brace <b>216</b> can be made inexpensively from metal or plastic by extrusion. The “X” shaped brace <b>216</b> can be fastened to the vertically extending stem <b>212</b> with a screw <b>220</b> or other device or method.
The “X” shaped brace <b>216</b> is coupled to and supports an LED support/heat sink <b>222</b>. A set of four screws <b>224</b> extend through holes <b>226</b> located at ends of the arms of the “X” shaped brace <b>216</b> and are screwed into holes (See <figref idrefs="DRAWINGS">FIG. 4</figref>) in the LED support/heat sink <b>222</b>. The LED support/heat sink <b>222</b> is hollow and is open at a bottom end <b>230</b> and a top end <b>232</b>. The LED support/heat sink <b>222</b> is suitably made out of an aluminum extrusion, although other materials, e.g., copper and other manufacturing methods, e.g., casting can be used. The LED support/heat sink <b>222</b> has heat sink fins <b>234</b> that extend inward into its hollow interior <b>235</b>. The LED support/heat sink <b>222</b> has four external faces <b>236</b> (two of which are visible in <figref idrefs="DRAWINGS">FIG. 2</figref>). Several LEDs <b>238</b> are mounted on each face <b>236</b>. Some of the heat sink fins <b>234</b> extend inward from behind each face, so that LEDs <b>238</b> mounted on each face are served by some of the heat sink fins <b>234</b>. Printed Circuits <b>240</b> for supplying power to the LEDs are formed on each face <b>236</b>. The printed circuits <b>240</b> lead to terminals <b>242</b> that extend into feed-throughs <b>244</b> located in holes in the faces <b>236</b>. Electrical wires <b>246</b> extend from the printed circuit board <b>208</b> through the stem <b>212</b>, through the hollow interior of the LED support/heat sink <b>222</b> to the terminals <b>242</b>. The wires can be fanned out (spliced to multiple branches) within the LED support/heat sink <b>222</b> in order to serve LEDs <b>238</b> on each face <b>236</b>. The wires can be terminated with terminals (not shown) that mate with the terminals <b>242</b> positioned in the feed-throughs <b>244</b>. Alternatively, wires can be run through drill holes and terminated on solder pads on the faces <b>236</b>. Connections between the faces can be made by wires, flexible printed circuits or soldered on terminals that bridge across corners. The printed circuits <b>240</b> can be formed on a thermally conductive, electrically insulating coating <b>248</b> which covers at least portions of the faces <b>236</b>. The coating <b>248</b> can be a plasma spayed alumina, an alumina layer formed by anodizing, or ceramic filled epoxy, for example. Other types of coatings known in the art may also be used. The printed circuits can be formed by screen printing or stencil a conductive ink that includes metal particles and the firing. Alternatively, the printed circuits can be formed by laminating a copper foil which is then patterned in a subtractive process, e.g., photolithography. Optionally the LED support/heat sink <b>222</b> can be part of the circuit supplying electrical power to the LEDs <b>238</b> (e.g., a ground return). Embedded passives (e.g., resistors, capacitors, inductors) may also be formed using the conductive coating of the LED support/heat sink <b>222</b>.
A bulb shaped cover <b>250</b> fits over the LED support/heat sink <b>222</b>. The bulb shaped cover <b>250</b> can be secured to the LED support/heat sink <b>222</b> by screws <b>252</b> or by other devices or methods. The LED support/heat sink <b>222</b> has threaded holes <b>253</b> for receiving the screws <b>252</b>. The bulb shaped cover <b>250</b> has an opening at its bottom <b>254</b> and an opening at its top <b>256</b>, so that it does not block air flow through the opening at the bottom <b>230</b> and the opening at the top <b>232</b> of the LED support/heat sink <b>222</b>. Note that the “X” shaped brace <b>216</b> also does not block air flow through the LED support/heat sink <b>222</b>.
In operation heat generated from the LEDs is conducted to the fins <b>234</b> and a convective flow of air flows axially through the hollow interior of the LED support/heat sink <b>222</b> passing over the fins and carrying away heat from the LEDs <b>238</b>. (In the perspective of <figref idrefs="DRAWINGS">FIG. 2</figref> the axial direction is vertical.) Although not shown in <figref idrefs="DRAWINGS">FIG. 1</figref> alternatively forced convection may be used.
The bulb shaped cover <b>250</b> can be diffuse or clear and the external faces <b>236</b> of the LED support/heat sink <b>222</b> can be given a highly polished (specular) or diffuse (matte) finish. For low intensity vanity lights a highly polished finish of the faces <b>236</b> in combination with a clear bulb shaped cover <b>250</b> is appealing and in this case warm white LEDs or a mixture of colored LEDs or white LEDs with some color LEDs added for warmth may be used. The shape of the bulb shaped cover <b>250</b> may be varied for ornamental effect.
Although as shown in <figref idrefs="DRAWINGS">FIG. 2</figref> the LED support/heat sink <b>222</b> has a square outside cross-sectional shape, alternatively the external cross-sectional shape is other than square, for example triangular, pentagonal, hexagonal or octagonal.
<figref idrefs="DRAWINGS">FIG. 3</figref> is a view of the LED light bulb <b>200</b> shown in <figref idrefs="DRAWINGS">FIG. 2</figref> in an assembled state. In <figref idrefs="DRAWINGS">FIG. 3</figref> arrows <b>302</b> represent convectively driven air flow flowing through the LED support/heat sink <b>222</b>. When the bulb <b>200</b> is positioned upright as shown in <figref idrefs="DRAWINGS">FIGS. 2-3</figref> the convectively driven air flow flows past the “X” shaped support <b>216</b> into the bottom end <b>230</b> of the LED support/heat sink <b>222</b>, along the heat sink fins <b>234</b>, and out the top end <b>232</b> of the LED support/heat sink <b>222</b>. As the air flows past the heat sink fins <b>234</b> it removes heat produced by the LEDs <b>238</b>. The heat sink fins <b>234</b> provide a large area for convective heat removal and the overall design provides this area without compromising the uniformity of the distribution of light produced by the bulb. Moreover, the design provides for continuous convectively driven air flow through the LED support/heat sink <b>222</b>. If the bulb <b>200</b> is mounted inverted the direction of air flow will reverse. If the bulb is oriented horizontally in which case hot air may be expelled at the top of both ends and cool air admitted at bottom of both ends, but likely without producing a clean longitudinal flow pattern. However, any slight tilt from horizontal should produce a longitudinal flow. Experiments have shown that operation of a prototype in the horizontal position leads to a temperature increase for LEDs on the upward facing surface that is less than 10° C., the temperature for the LEDs on side facing sides and the downward facing side being lower.
<figref idrefs="DRAWINGS">FIG. 4</figref> is an end view of an extruded segment <b>402</b> of an LED support/heat sink according to an embodiment of the invention. The segment <b>402</b> is designed to nest with identical segments to form a complete LED support/heat sink. Each segment <b>402</b> includes a face <b>404</b> on which LEDs <b>238</b> are mounted and which in an assembled LED support/heat sink will face outward and heat sink fins <b>406</b> which in an assembled LED support/heat sink will project inward as in the case of <figref idrefs="DRAWINGS">FIGS. 2-3</figref>. Nesting is achieved by having a concave end <b>408</b> and a complementary convex end <b>410</b>, however one skilled in the art of extrusion will appreciate that many alternative nesting, snap-fit, slip-fit or interlocking geometries are possible. The screw holes <b>228</b> are provided in the convex end <b>410</b>. The “X”-shaped brace <b>216</b> and the bulb shaped cover <b>250</b> will help to hold the interlocking segments <b>402</b> together. Although not shown in <figref idrefs="DRAWINGS">FIG. 1</figref>, in the case of a LED support/heat sink made of multiple segments, optionally another brace can be used at the top end. On the other hand the bulb shaped cover <b>250</b> may be relied on to provide mechanical support at the top end of a multi segment LED support/heat sink.
Making the LED support/heat sink out of multiple segments allows all the LEDs <b>238</b> to be soldered in a reflow soldering operation while the faces <b>404</b> are facing up. In the case that the LED support/heat sink is not made of multiple segments the LEDs can be held in place by a fixture while the solder is brought up to melting temperature, or solders having successively lower melting temperatures can be used to solder LEDs on successive faces <b>236</b>, or a process that uses localized heating may be used. If localized heating (e.g., hot bar soldering) is used one way to attach packaged LEDs to the LED support/heat sink <b>222</b> would be to equip a pick and place machine with a computer operated rotary indexer which would sequentially present faces of the LED support/heat sink to robotic arms of the pick and place machine.
<figref idrefs="DRAWINGS">FIG. 5</figref> shows four of the segments <b>402</b> after printed circuits <b>240</b> have been formed on the faces <b>404</b>, and two LEDs <b>238</b> have been mounted on the faces <b>404</b> and soldered (or affixed with conductive adhesive) to the printed circuits <b>240</b>. The printed circuits <b>240</b> on each face <b>404</b> include an anode connection printed circuit <b>502</b> and a cathode connection printed circuit <b>504</b>. The cathode printed circuit <b>504</b> has a cathode bus line segment <b>506</b> extending horizontally (in the perspective of <figref idrefs="DRAWINGS">FIG. 4</figref>) proximate the top end of the face <b>404</b> and similarly the anode printed circuit <b>502</b> has an anode bus line segment <b>508</b> extending horizontally proximate the bottom end of the face <b>404</b>. The bus line segments <b>506</b>, <b>508</b> of the different segments <b>402</b> are connected by soldered bendable strips <b>510</b>, which can for example be made from copper or brass or other conductive material. In lieu of the bendable strips wires with flat terminals or segments of flex circuit may be used. The left most segment <b>402</b> in <figref idrefs="DRAWINGS">FIG. 4</figref> is provided with the contact terminals <b>242</b> which are positioned in the insulated feed throughs <b>244</b> and make contact with the printed circuits <b>502</b>, <b>504</b> for supplying power thereto. It is unnecessary to drill (or otherwise form) holes for the insulted feed throughs <b>244</b> in the remaining segments <b>402</b>. A set of four (or more) segments with LEDs <b>238</b>, bendable strips <b>510</b> and contact terminals <b>242</b> in position as shown in <figref idrefs="DRAWINGS">FIG. 5</figref> can be put through a solder reflow oven held in a jig in order to make a complete assembly which when complete can be folded up to make an LED support/heat sink.
In <figref idrefs="DRAWINGS">FIG. 5</figref> all of the LEDs <b>238</b> are connected in parallel. Alternatively, the LEDs <b>238</b> are connected in series or, as a further alternative in a series-parallel network. One possible form of series-parallel network would have all of the LEDs <b>238</b> on each individual face <b>404</b> in series and have the circuits of the multiple faces <b>404</b> connected in parallel. Having all the LEDs <b>238</b> connected in series leaves the light bulb <b>200</b> vulnerable to complete failure if an open circuit defect develops anywhere in the LED circuit, but on the other hand reduces the current output requirement for the LED driver circuit on the printed circuit board <b>208</b>. A series-parallel network is thus a good compromise between robustness to single-point failure and reducing current requirement for the LED driver circuit and parts of the power distribution network. A series-parallel arrangement may also be preferred in order to match the output impedance of a driver circuit.
Other possibilities for the fins of the LED support/heat sink include cross-cut extruded fins, pin fins, folded fins, stacked fins, skeaved fins and a new fin construction that comprises an assembly of stacked stamped plates in which at least some of the stamped plates include fin profiles. Some of these are described below and shown in the FIGs.
<figref idrefs="DRAWINGS">FIG. 6</figref> includes one segment <b>602</b> of an extruded LED support/heat sink that has cross cut fins <b>604</b>.
<figref idrefs="DRAWINGS">FIG. 7</figref> shows one segment of an LED support/heat sink <b>702</b> along with an associated X-shaped brace <b>704</b>. The complete LED support/heat sink would have four such segments, however alternatively it could have a different number of segments in which case the X-shaped brace <b>704</b> would be modified to have a different number of radial arms. This LED supported/heat sink, which can be made from copper or aluminum for example, includes a folded fin <b>706</b> thermally connected to a base plate <b>708</b>. The folded fin <b>706</b> can be thermally connected to the base plate <b>708</b> by brazing, soldering, by thermal grease or a thermally conductive adhesive, for example. The folded fin <b>706</b> is shaped as a square wave with a triangular envelope. The folded fin <b>706</b> can be made by roll forming. Copper has a higher thermal conductivity than aluminum and the folded fin design provides one way to make the LED support/heat sink from copper. The X-shaped brace <b>704</b> includes a number of threaded drilled holes <b>710</b> that align with holes <b>710</b> in the base plate <b>708</b> and screws <b>714</b> are used to secure the two together. Rather than having square corners at the tips of the fins a radiused form could be used.
<figref idrefs="DRAWINGS">FIG. 8</figref> is a plan view of one segment <b>802</b> of an LED support/heat sink that includes an array of pin fins <b>804</b> (two of which are identified by reference numeral to avoid crowding the FIG.)
<figref idrefs="DRAWINGS">FIG. 9</figref> shows an end view of an LED support/heat sink segment <b>900</b> with a branched heat sink fin according to an embodiment of the invention. The branched heat sink fin comprises a main fin <b>904</b> extending from a base <b>902</b> and a plurality of branch fins <b>906</b> extending from the main fin <b>904</b>. One or more LEDs <b>908</b> (one of which is visible in <figref idrefs="DRAWINGS">FIG. 9</figref>) are mounted on an outside surface <b>910</b> of the segment <b>900</b> proximate the juncture of the base <b>902</b> and the main fin <b>904</b>. Although not shown in <figref idrefs="DRAWINGS">FIG. 9</figref> all or parts of the branched heat sink fit can be cross cut.
<figref idrefs="DRAWINGS">FIG. 10</figref> includes one segment <b>1002</b> of an LED support/heat sink. This segment includes a set of stacked fins <b>1008</b> that are attached to a base plate <b>1006</b>. The fins <b>1008</b> have different height and are arranged in order to produce the triangular envelope profile shown in <figref idrefs="DRAWINGS">FIG. 10</figref>. The fins may be attached by brazing, soldering or using thermally conductive adhesive, for example.
<figref idrefs="DRAWINGS">FIG. 11</figref> shows a LED support/heat sink segment <b>1102</b> according to an alternative embodiment. The segment <b>1102</b> includes a base <b>1104</b> to which a plurality of heat sink fins <b>1106</b> are clamped using narrow elongated clamping plate <b>1108</b> and screws <b>1110</b>. The heat sink fins <b>1106</b> are sheets of heat conductive material such as copper or aluminum, which are clamped along their centerlines and bent away from the base <b>1104</b>. Each heat sink fin <b>1106</b> is bent at a different angle as shown. The clamping plate <b>1108</b> includes holes <b>1112</b> for the screws <b>1110</b> and the fins <b>1106</b> include corresponding holes which are not visible in the figure. The base <b>1104</b> includes corresponding threaded holes, that are not visible, into which the screws <b>1110</b> thread. A region of the base <b>1104</b> under the clamping plate <b>1108</b>, the underside of the clamping plate <b>1108</b> and the areas of the fins <b>1106</b> that are clamped are suitably coated with thermal adhesive or thermal grease. Alternatively, solder or brazing can be used. LEDs (not visible in <figref idrefs="DRAWINGS">FIG. 11</figref>) are suitably mounted on the front face (bottom face in <figref idrefs="DRAWINGS">FIG. 11</figref>) of the base overlying or proximate the clamping plate <b>1108</b>. The clamping plate <b>1108</b> is suitably made of a thermally conductive material such as copper or aluminum so that it contributes to longitudinal conduction of heat away from the LEDs.
<figref idrefs="DRAWINGS">FIG. 12</figref> is an exploded view of an LED bulb <b>1200</b> showing some alternative features according to an embodiment of the invention and <figref idrefs="DRAWINGS">FIG. 13</figref> is a partial sectional view of the bulb shown in <figref idrefs="DRAWINGS">FIG. 12</figref>. Starting from the bottom of <figref idrefs="DRAWINGS">FIG. 12</figref>, the bulb includes an Edison style base <b>1202</b> attached to a lower housing <b>1204</b>. The lower housing <b>1204</b> includes a D-shaped recess <b>1206</b> for receiving a D-shaped stem <b>1208</b>. According to alternative embodiments a stem and lower housing are made in one piece. The stem <b>1208</b> fits into a D-shaped central hole <b>1210</b> of an X-shaped brace <b>1212</b>. According to alternative embodiments a stem and an X-shaped brace are made in one piece. Four U-shaped screw bosses <b>1214</b> are located at ends of four arms of the X-shaped brace <b>1212</b>. The U-shape of the bosses <b>1214</b> is better adapted for extrusion than would be closed holes, allowing the X-shaped brace <b>1212</b> to be made inexpensively. A set screw <b>1211</b> helps secure the X-shaped brace <b>1212</b> to the stem <b>1208</b>. Four LED support/heat sink segments <b>1216</b> interlink together to form a square LED support/heat sink. Each segment <b>1216</b> has a male interlinking portion <b>1218</b> on one side and a complementary female interlinking portion <b>1220</b> on an opposite side. The male portion <b>1218</b> has a semi-circular x-section outside surface and the female interlinking portion <b>1220</b> has a semi-circular x-section inside surface. A portion of the male portion <b>1218</b> at both the top and bottom ends of the segments <b>1216</b> is trimmed away to leave an empty space in the female interlinking portion <b>1220</b>. These spaces will serve as screw bosses for receiving a lower set of screws <b>1222</b> and an upper set of screws <b>1224</b> (e.g., self-tapping screws). A square upper brace <b>1226</b> includes internal corner cut-out portions <b>1228</b> for the upper set of screws <b>1224</b> to pass through. A lower bulb-shaped cover <b>1230</b> and an upper bulb-shaped cover <b>1232</b> fit together at half-lap edges <b>1234</b> forming a complete bulb shaped cover. Alternatively one or both of the bulb shaped covers <b>1230</b>, <b>1232</b> can be made with a radially undulating edge so that contact between the two is only made at points thereby allowing for the passage of convectively driven air through radial gaps between the points. When assembled the upper set of screws <b>1224</b> pass through a set of holes <b>1236</b> in the upper bulb-shaped cover <b>1232</b> through a set of spacers <b>1238</b> through the cut-out portions <b>1228</b> and into the female interlinking portions <b>1220</b> of the segments <b>1216</b>. The lower set of screws <b>1222</b> pass through holes (not shown) in the lower bulb-shaped cover <b>1230</b>, through the U-shaped screw bosses <b>1214</b> of the X-shaped brace <b>1212</b> and through a set of spacers <b>1240</b> and into the female interlinking portions <b>1220</b> of the LED support/heat sink segments <b>1216</b>.
As shown in <figref idrefs="DRAWINGS">FIGS. 12 and 13</figref> two LEDs <b>1242</b> are mounted on each LED support/heat sink segment <b>1216</b> for a total of eight LEDs. The eight LEDs can be operated at 10 watts at an acceptably low temperature while providing an adequate amount of light for replacing a conventional incandescent bulb. As LED efficacy improves greater light output will be possible. Alternatively only one LED is used on each segment <b>1216</b>.
As shown each LED <b>1242</b> comprises an LED chip mounted on a large substrate <b>1244</b> and surrounded by a large primary lens <b>1246</b>. The primary lens and an alternative secondary lens are described below. The lenses serve to distribute light from the LED chips more evenly that the quasi-Lambertian distribution produced by an LED chip with an ordinary hemispherical primary lens. Because the lenses can redistribute the light substantially as needed, the design of the LED support/heat sink can be optimized for heat dissipation, there being no need to place LEDs in a top position where they would interfere with the free convective flow afforded by the open LED support/heat sink design.
As shown in <figref idrefs="DRAWINGS">FIG. 13</figref> convectively driven air flow indicated by streamline <b>1302</b> can flow past the X-shaped brace <b>1212</b> into the space between the support/heat sink segments <b>1216</b> and the bulb shaped covers <b>1230</b>, <b>1232</b>, between the spacers <b>1238</b> and out of the bulb <b>1200</b>, thus allowing the external faces of the segments <b>1216</b> to contribute to heat dissipation. At the same time, as indicated by light rays shown in <figref idrefs="DRAWINGS">FIG. 13</figref>, the bulb shaped covers <b>1230</b>, <b>1232</b> fully surround the LEDs optically, so that all light from the LEDs will be diffused in the case that the diffusive bulb shaped covers <b>1230</b>, <b>1232</b> are used.
<figref idrefs="DRAWINGS">FIG. 14</figref> shows an LED light bulb <b>1400</b> according to an alternative embodiment of the invention. In this embodiment a circuit board <b>1402</b> that includes at least part of the LED driver circuit is positioned within (along the diagonal) of an LED support/heat sink <b>1404</b>. In this case a smaller housing <b>1406</b> is used. The volume enclosed by the Edison style base <b>204</b> and the smaller housing <b>1406</b> can still be used to enclose some circuit components, for example a bulky magnetic components such as inductors or transformers.
<figref idrefs="DRAWINGS">FIG. 15</figref> shows an LED light bulb <b>1500</b> according to a further alternative embodiment of the invention. In this case the stem <b>212</b> and the “X” shaped brace <b>216</b> are not utilized. Instead, an LED support/heat sink <b>1502</b> with internal heat sink fins <b>234</b> extends directly from a lower assembly <b>1504</b>. The lower assembly <b>1504</b> includes an Edison style base <b>204</b> attached to a lower housing part <b>1506</b> which attaches to an upper housing part <b>1508</b>. The LED support/heat sink <b>1502</b> fits into a complementary shaped (e.g., square, pentagonal) opening <b>1510</b> in the upper housing part <b>1508</b>. The lower housing part <b>1506</b> and the upper housing part <b>1508</b> enclose a circuit board <b>1512</b> that includes an LED driver circuit. The housing parts <b>1506</b>, <b>1508</b> can be made inexpensively by injection molding plastic. A two-piece bulb shaped cover <b>1514</b> fits over the LED support/heat sink <b>1502</b> and is secured thereto by one or more screws <b>1516</b> or by other fastening devices or methods. The bulb shaped cover <b>1514</b> includes an upper half <b>1518</b> and a lower half <b>1520</b> joined at the equator, e.g., by snap fitting as known in the art of plastic design. Except, perhaps for ornamental bulbs, the bulb shaped cover <b>1514</b> has a rounded shape. The bulb shaped cover <b>1514</b> can also be made inexpensively by injection molding plastic. Alternatively the bulb shaped cover can be made by blow molding followed by trimming (e.g., machining) to form top and bottom openings. The bulb shape cover can also be made of glass although at greater expense.
In order to provide convectively driven longitudinal air flow through the LED support/heat sink <b>1502</b> side openings <b>1522</b> are formed on the faces <b>1524</b> of the LED support/heat sink <b>1502</b> proximate the upper housing part <b>1508</b> of the lower assembly <b>1504</b>. Heated air, carrying heat transferred from the LEDs <b>238</b> through the fins <b>234</b> will rise out of the top end <b>232</b> of the LED support/heat sink <b>1502</b> and cool air will be drawn into the openings <b>1522</b>. If the bulb <b>1500</b> is inverted the flow direction will reverse. The openings <b>1522</b> can be formed by spot facing with an end mill in an automated machining center. Although the openings <b>1522</b> as shown are circular, alternatively other shapes can be used, for example slots, or squares with rounded corners. These shapes can also be machined with an end mill. By eliminating the stem <b>212</b> and the “X” shaped brace <b>216</b> the part count of the bulb <b>1500</b> is reduced.
<figref idrefs="DRAWINGS">FIG. 16</figref> is perspective view of an LED light bulb <b>1600</b> according to a still further embodiment of the invention. The LED light bulb <b>1600</b> comprises a lower housing <b>1602</b> including an Edison base <b>204</b>. The lower housing <b>1602</b> is connected via a hollow stem <b>1604</b> to a hollow LED support/heat sink <b>1606</b>. The LED support/heat sink <b>1606</b> is made up extruded (e.g., aluminum) segments <b>1608</b>, <b>1610</b>, <b>1612</b> and <b>1614</b>. In this case the extrusion direction is perpendicular to the longitudinal axis of the LED light bulb <b>1600</b>. (The longitudinal axis is parallel to the hollow stem <b>1604</b>.) The segments <b>1608</b>, <b>1610</b>, <b>1612</b> and <b>1614</b> include a lower segment <b>1608</b> and upper segment <b>1610</b>, a left segment <b>1612</b> and a right segment <b>1614</b>. The left segment <b>1612</b> and the right segment <b>1614</b> can be the same extrusion. The lower segment <b>1608</b> has a hole <b>1609</b> drilled (or otherwise formed) in a boss <b>1616</b> to receive the top end of the hollow stem <b>1604</b>. The hole <b>1609</b> can be stepped down at the end so the stem <b>1604</b> will be prevented from passing completely through, while at the same time allowing power supply wires <b>1618</b> to pass through. The segments <b>1608</b>, <b>1610</b>, <b>1612</b> and <b>1614</b> come together at interlocking corner joints. The upper segment <b>1610</b>, the left segment <b>1612</b> and the right segment <b>1614</b> include heat sink fins <b>1620</b> that extend inward into a space formed in the middle of the joined segments <b>1608</b>, <b>1610</b>, <b>1612</b> and <b>1614</b>. Optionally the lower segment <b>1608</b> also includes inwardly extending heat sink fins. The segments <b>1608</b>, <b>1610</b>, <b>1612</b> and <b>1614</b> include external faces <b>1622</b>. LEDs <b>1624</b> (only two of which are numbered to avoid crowding the drawing) are mounted on one or more of the external faces <b>1622</b>. According to one embodiment the LEDs <b>1624</b> are mounted on the faces <b>1622</b> of the side segments <b>1612</b>, <b>1614</b> and upper segment <b>1610</b>. Optionally LEDs <b>1624</b> can also be mounted on the lower segment <b>1608</b>. If a secondary optic (not shown) that makes the light output from the LEDs <b>1624</b> more uniform than the bare Lambertian distribution is used, then a sufficiently uniform overall light distribution may be obtained from LEDs <b>1624</b> mounted only on the side segments <b>1612</b>, <b>1614</b>. In such a case the heat sink fins <b>1620</b> of the upper segment <b>1610</b> can be reduced in size or eliminated in order to allow the heat sink fins <b>1620</b> of the side segments <b>1612</b><b>1614</b> to be increased in size, thereby affording increased cooling for the LEDs <b>1624</b>. A light transmissive cover <b>1626</b> that has the shape of a “U” shaped cross section extruded along a “U” shaped path fits over the LED support/heat sink <b>1606</b>. The cover <b>1626</b> is secured with a set of screws <b>1628</b> (or other fastening device or method.) The cover <b>1626</b> allows free access to the heat sink fins <b>1620</b> allowing convective heat transfer to take place.
In white LEDs that include a phosphor in close proximity to the LED chip, some phosphor converted light may be back-scattered to the LED light and absorbed thereby reducing the LEDs efficacy.
<figref idrefs="DRAWINGS">FIGS. 17</figref>, <b>18</b> show a bulb shaped cover <b>1702</b> according to an alternative embodiment of the invention. According to the alternative embodiment of the invention rather than using LEDs that incorporate the phosphor; excitation (e.g., blue or UV) LEDs are used in combination with the bulb shaped <b>1702</b> cover shown in <figref idrefs="DRAWINGS">FIGS. 17-18</figref> which includes a coating <b>1704</b> that includes phosphor particles <b>1802</b> (only two of which are numbered to avoid crowding the drawing) dispersed in a transparent binder <b>1804</b>. Alternatively the phosphor particles are dispersed in the bulk of the material of the bulb shaped cover <b>1802</b>.
According to certain embodiments, e.g., higher power smaller bulbs, passive cooling may be insufficient, however the designs described above lend themselves to active cooling. <figref idrefs="DRAWINGS">FIG. 19</figref> shows an omnidirectional light bulb <b>1900</b> that includes active cooling. The bulb <b>1900</b> includes a bulb shaped cover <b>1902</b> that includes an upper part <b>1904</b> that extends above an LED support/heat sink <b>1906</b>. The extending portion of the upper part accommodates a cooling fan <b>1908</b> (shown detached in <figref idrefs="DRAWINGS">FIG. 19</figref> for clarity). The cooling fan <b>1908</b> is suitably supplied by wires (not shown) that extend up through the LED support/heat sink <b>1906</b>. The cooling fan <b>1908</b> can be driven based on a reading of a temperature sensor (not shown). Four screws <b>1910</b> are provided for securing the cooling fan <b>1908</b> to the LED support/heat sink <b>1906</b>. Alternatively, in lieu of a cooling fan, a corona discharge air pump is used. Such devices are sometimes called “corona wind” or “ion wind” devices.
A portion of the upper part <b>1904</b> of the bulb shaped cover <b>1902</b> is shown broken away to reveal an inner depending skirt <b>1911</b> that extends downward in overlapping relation to the LED support/heat sink <b>1906</b>. A seal <b>1912</b> is provided between the depending skirt <b>1911</b> and the LED support/heat sink <b>1906</b>. A similar seal (not shown) would be provided at the bottom of the Led support/heat sink forming a sealed space. The seal <b>1912</b> may take the form of a gasket, or sealing compound for example. A lower part <b>1914</b> of the bulb shaped cover <b>1902</b> includes two tipoffs <b>1916</b> which are used to flush air out of the interior of the bulb shaped cover and fill the interior with a dry inert gas (e.g., nitrogen, rare gas). Doing so will avoid condensation in the vicinity of the LEDs and control oxidative degradation of the LEDs or circuitry supplying the LEDs. The tipoffs <b>1916</b> can be sealed by crimping with a heated tool or using another device or method. A joint <b>1918</b> between the upper part <b>1904</b> and lower part <b>1914</b> of the bulb shaped cover <b>1902</b> is suitably sealed with a sealant, e.g., silicone or using another device or method.
In the embodiments shown above the LEDs <b>238</b> are directly attached to the LED support/heat sink <b>222</b>, <b>602</b>, <b>900</b>, <b>1002</b>. Alternatively, especially for initial production, the LEDs can be mounted on a small printed circuit board which is in turn attached to the LED support heat sink <b>222</b>, <b>602</b>, <b>900</b>, <b>1002</b>, e.g., with screws, however doing so introduces additional thermal resistance.
For omnidirectional LED light bulbs it is appropriate to provide a relatively uniform distribution of light. <figref idrefs="DRAWINGS">FIG. 20</figref> shows a generatrix <b>2002</b> of an outer lens surface of a primary lens for an LED that is designed to provide a more uniform distribution of light than the typical hemispherical primary lens or other primary lenses such as the side-emitting primary lens or the “batwing” primary lens. The axes in <figref idrefs="DRAWINGS">FIG. 20</figref> and <figref idrefs="DRAWINGS">FIG. 21</figref> are millimeters. The lens represented in <figref idrefs="DRAWINGS">FIG. 20</figref> is taught in my issued U.S. Pat. No. 8,339,716 entitled “Illumination Lenses Including Light Redistributing Surfaces”. The lenses <b>1246</b> used in the embodiment shown in <figref idrefs="DRAWINGS">FIG. 12</figref> and in other embodiments can be of this design. The lens surface is obtained by revolving the generatrix about the Z-axis shown in <figref idrefs="DRAWINGS">FIG. 20</figref>. The lens is described by the following differential equation:
<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mfrac><mo>∂</mo><mrow><mrow><mo>∂</mo><mi>ϕ</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mfrac><mo></mo><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>=</mo><mfrac><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow><mo>-</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mrow><mo>-</mo><mi>n</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ2</mi><mo>-</mo><mi>ϕ1</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac></mrow></mtd><mtd><mrow><mi>DE</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow></mtd></mtr></mtable></math></maths><br /> Where,
r1 is a radial coordinate of the lens surface;
phi1 is a polar (zenith) angle coordinate of the lens surface, and is also the domain (independent) variable over which the above equation is defined (see <figref idrefs="DRAWINGS">FIG. 20</figref>);
n1 is the index of refraction of the lens defined by the equation;
n2 is the index of refraction of the surrounding medium (e.g., of air) which usually equals 1 and
phi2 is the polar angle variable for a predetermined specified output light intensity and is equal to the polar angle of an ideal ray (a ray emitted at the origin of the X-Z coordinate system shown in <figref idrefs="DRAWINGS">FIG. 20</figref>) that was initially emitted at angle phi1 after the ray has left the surface of each lens defined by the equation (see <figref idrefs="DRAWINGS">FIG. 20</figref>) and is given by:
<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mtable><mtr><mtd><mrow><mfrac><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ1_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msubsup><mo></mo><mrow><mi>rad_in</mi><mo></mo><mrow><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ1_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mi>_MAX</mi></mrow></msubsup><mo></mo><mrow><mi>rad_in</mi><mo></mo><mrow><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ2_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msubsup><mo></mo><mrow><mi>rad_out</mi><mo></mo><mrow><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mrow><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ2_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mi>_MAX</mi></mrow></msubsup><mo></mo><mrow><mi>rad_out</mi><mo></mo><mrow><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mrow></mfrac></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow></mtd></mtr></mtable></math></maths>
where,
phi1_MIN and phi1_MAX are the lower and upper polar angle limits respectively of light collected by each lens defined by DE1;
phi2_MIN and phi2_MAX are the lower and upper polar angle limits respectively of a predetermined specified output light intensity distribution for each lens defined by the DE1;
rad_in(phi1) is the light intensity distribution (e.g., quasi-Lambertian) of the LED for which the lens is designed; and
rad_out(phi2) is the predetermined specified output light intensity distribution for each lens defined by the equations;
with initial conditions r1_ini for r1.
DE1 is integrated numerically and EQU. 1 is solved numerically for each input value of phi1, as needed, during the integration.
Table 1 below includes the parameters and light distribution functions corresponding to <figref idrefs="DRAWINGS">FIG. 20</figref>.
<tables id="TABLE-US-00001" num="00001"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="3"><colspec colname="1" colwidth="28pt" align="left" /><colspec colname="2" colwidth="70pt" align="left" /><colspec colname="3" colwidth="119pt" align="left" /><thead><row><entry namest="1" nameend="3" rowsep="1">TABLE I</entry></row><row><entry namest="1" nameend="3" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /><entry>Phi1_MIN</entry><entry>0.0 radians</entry></row><row><entry /><entry>Phi1_MAX</entry><entry>1.57 radians (90 degrees)</entry></row><row><entry /><entry>Phi2_MIN</entry><entry>0.0 radians</entry></row><row><entry /><entry>Phi2_MAX</entry><entry>1.57 radians (90 degrees)</entry></row><row><entry /><entry>rad_in(phi1)</entry><entry>Quasi Lambertian measured</entry></row><row><entry /><entry /><entry>data</entry></row><row><entry /><entry>rad_out(phi2)</entry><entry>=1.0 (Uniform Intensity Goal)</entry></row><row><entry /><entry>r1_ini</entry><entry>3.0</entry></row><row><entry /><entry>n1</entry><entry>1.4</entry></row><row><entry /><entry>n2</entry><entry>1.0</entry></row><row><entry namest="1" nameend="3" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>
Note that rad_in(phi1) was based on measurements of an LED with a hemispherical primary lens and is approximately equal to the ideal Lambertian distribution which is cos(phi1).
The shape of the lens surface transforming a Lambertian distribution to a uniform distribution given by DE1 (half of which is shown in <figref idrefs="DRAWINGS">FIG. 20</figref>) can be broadly described as half of an oval.
The lens has a calculated transmittance of 96.7% with only small Fresnel losses at the single surface. Some of the light reflected by the single surface will be recovered by being scattered back out of the lens.
The lens is not expected to produce perfect uniformity due to the finite size of the LED chip and due to edge effects occurring at the limit of the angular range of the lens (φ=90°. Any non-uniformities will be diminished by using a bulb shaped cover (e.g., 250) that is diffusive, because a diffusive bulb shaped cover acts as a low pass filter in the domain of φ2 integrating deviations from the average intensity level.
Note that by arranging two LEDs with such lenses facing in opposite directions the full solid angle (4π steradian) about the arrangement will be illuminated. Thus by providing LEDs on four sides of the LED support/heat sinks described above the full solid angle (4π steradian) is covered redundantly.
The LEDs used in the bulbs described above can be white LEDs and/or color LEDs.
According to an alternative embodiment LEDs with common hemispherical primary lenses are used in combination with secondary lenses that redistribute the light emitted by the LEDs more uniformly than the bare LED. <figref idrefs="DRAWINGS">FIG. 21</figref> a generatrix of an inner surface <b>2102</b> and a generatrix of an outer surface <b>2104</b> of such a secondary lens. The lens is described in issued U.S. Pat. No. 8,405,920 entitled “ILLUMINATION LENSES”. The lenses surfaces are mainly described by a set of coupled differential equations DE2 and DE3, however a portion <b>2106</b> of the first surface defined by DE2 would curve inward leading to manufacturing difficulties and so is replaced with a constant draft (conical) portion <b>2108</b> and to compensate for this alteration in the first surface a portion of the second surface <b>2110</b> is replaced with a portion <b>2112</b> redefined by DE4 given below. The equations are:
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/></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mn>3</mn></msup></mfrac></mrow></mrow><mo>)</mo></mrow></mrow><mrow><mrow><mo>(</mo><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msup><mi>%2</mi><mrow><mo>(</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>)</mo></mrow></msup></mrow></mfrac></mrow></mrow><mo>)</mo></mrow></mrow><mo>/</mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>1</mn><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><msup><mrow><mo>(</mo><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%2</mi></mrow></mfrac></mrow></msqrt></mrow><mo>+</mo><mfrac><mrow><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%5</mi></mrow><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>2</mn><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%5</mi></mrow><msup><mrow><mo>(</mo><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mn>2</mn></msup></mfrac></mrow><mi>%2</mi></mfrac></mrow><mo>)</mo></mrow><mo>/</mo><mi>r</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow><mo>/</mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><msup><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%4</mi><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><msup><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow></msqrt></mrow></mrow><mo>)</mo></mrow><mo>/</mo><mstyle><mtext /></mstyle><mo></mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%3</mi><mo>-</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%4</mi><mo>)</mo></mrow></mrow></mrow><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mo></mo><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%4</mi><mo>)</mo></mrow></mrow></mrow><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo></mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><msup><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%4</mi><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><msup><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow></msqrt></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%1</mi><mo></mo><mstyle><mtext>:</mtext></mstyle><mo>=</mo></mrow><mo>-</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mi>ϕ1</mi></mrow><mo>+</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mrow><mi>ϕ3</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%2</mi><mo></mo><mstyle><mtext>:</mtext></mstyle><mo>=</mo><mn>1</mn></mrow><mo>+</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>2</mn><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><msup><mrow><mo>(</mo><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mn>2</mn></msup></mfrac></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%3</mi><mo></mo><mstyle><mtext>:</mtext></mstyle></mrow><mo>=</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mo>(</mo><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mo></mo><msqrt><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>2</mn></mrow></msqrt></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%4</mi><mo></mo><mstyle><mtext>:</mtext></mstyle><mo>=</mo></mrow><mo>-</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>3</mn></mrow><mo>+</mo><mrow><mi>arctan</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%5</mi><mo></mo><mstyle><mtext>:</mtext></mstyle></mrow><mo>=</mo><mrow><mrow><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo>+</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mrow><mo>(</mo><mrow><mfrac><mo>∂</mo><mrow><mo>∂</mo><mi>ϕ1</mi></mrow></mfrac><mo></mo><mrow><mi>ϕ3</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>DE</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>3</mn></mrow></mtd></mtr></mtable></math></maths><br /> Where: <br /> n2 is the index of refraction of the lens defined by the equations; <br /> n1 is the index of refraction of the surrounding medium (e.g., of air) which usually equals 1; <br /> phi1 is the polar angular coordinate (zenith angle) of the first lens surface; phi3 is the polar angle (zenith angle) of an ideal ray (a ray emitted at the origin) that was initially emitted at angle phi1 after the ray has left the second surface of each lens defined by the equations (see <figref idrefs="DRAWINGS">FIG. 21</figref>) and is given by:
<maths id="MATH-US-00004" num="00004"><math overflow="scroll"><mtable><mtr><mtd><mrow><mfrac><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ1_</mi><mo></mo><mi>MIN</mi></mrow><mi>ϕ1</mi></msubsup><mo></mo><mrow><mi>rad_in</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ1</mi></mrow></mrow></mrow><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ1_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ1_</mi><mo></mo><mi>MAX</mi></mrow></msubsup><mo></mo><mrow><mi>rad_in</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ1</mi></mrow></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ3_</mi><mo></mo><mi>MIN</mi></mrow><mi>ϕ3</mi></msubsup><mo></mo><mrow><mi>rad_out</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ3</mi></mrow></mrow></mrow><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ3_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ3_</mi><mo></mo><mi>MAX</mi></mrow></msubsup><mo></mo><mrow><mi>rad_out</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ3</mi></mrow></mrow></mrow></mfrac></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>2</mn></mrow></mtd></mtr></mtable></math></maths><br /> where, <br /> phi1_MIN and phi1_MAX are the lower and upper polar angle limits respectively of light collected by each lens defined by the equations; <br /> phi3_MIN and phi3_MAX are the lower and upper limits respectively of a predetermined specified output light intensity distribution for each lens defined by the equations; <br /> rad_in(phi1) is the light intensity distribution of the light source (e.g., LED) for which the lens is designed; and <br /> rad_out(phi3) is the predetermined specified output light intensity distribution for each lens defined by the equations; <br /> phi2 is a polar angular coordinate of the second lens surface and is given by:
<maths id="MATH-US-00005" num="00005"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>ϕ2</mi><mo>=</mo><mrow><mi>ϕ1</mi><mo>+</mo><mrow><mi>arcsin</mi><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mi>n</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mo></mo><msqrt><mrow><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>2</mn><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><msup><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mi>n</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mn>2</mn></msup></mfrac><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfrac><mo>)</mo></mrow><mo>-</mo><mrow><mi>arctan</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mrow><mo>-</mo><mi>n</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac><mo>)</mo></mrow></mrow><mo>-</mo><mrow><mi>arcsin</mi><mo>(</mo><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo></mo><mrow><mrow><mi>sin</mi><mo>(</mo><mrow><mi>arcsin</mi><mo></mo><mtable><mtr><mtd><mrow><mrow><mo>(</mo><mfrac><mrow><mo>(</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mi>n</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mo></mo><msqrt><mrow><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>2</mn><mn>2</mn></msup><mo></mo><msup><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><msup><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mi>n</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow><mo>)</mo></mrow><mn>2</mn></msup></mfrac><mo>+</mo><mn>1</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mfrac><mo>)</mo></mrow><mo>-</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>arctan</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>%1</mi><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mrow><mo>)</mo></mrow><mo>/</mo><mi>r</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%1</mi><mo></mo><mstyle><mtext>:</mtext></mstyle><mo>=</mo></mrow><mo>-</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mi>ϕ1</mi></mrow><mo>+</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mrow><mi>ϕ3</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mi>and</mi></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>3</mn></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mo>∂</mo><mi>ϕ3</mi></mrow><mrow><mo>∂</mo><mi>ϕ1</mi></mrow></mfrac><mo>=</mo><mrow><mrow><mo>(</mo><mfrac><mrow><mi>rad_in</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow></mrow><mrow><mi>rad_out</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow></mrow></mrow></mrow></mfrac><mo>)</mo></mrow><mo>·</mo><mrow><mo>(</mo><mfrac><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ3_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ3_</mi><mo></mo><mi>MAX</mi></mrow></msubsup><mo></mo><mrow><mi>rad_out</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ3</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ3</mi></mrow></mrow></mrow><mrow><msubsup><mo>∫</mo><mrow><mi>ϕ1_</mi><mo></mo><mi>MIN</mi></mrow><mrow><mi>ϕ1_</mi><mo></mo><mi>MAX</mi></mrow></msubsup><mo></mo><mrow><mi>rad_in</mi><mo></mo><mrow><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo>·</mo><mn>2</mn></mrow><mo></mo><mrow><mi>π</mi><mo>·</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mo>ⅆ</mo><mi>ϕ1</mi></mrow></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>4</mn></mrow></mtd></mtr></mtable></math></maths><br /> with initial conditions r1_ini and r2_ini for r1(phi1) and r2(phi1) respectively
EQU. 2 is solved numerically for to obtain a value of phi3 for each input value of phi1 and DE1 and DE2 are integrated numerically, e.g., using the Runge Kutta integrator.
If phi1_min=phi3_min=0, EQU. 4 will be undefined at phi1_min=0. In this case, instead of using EQU. 4 one can use the values of phi3 obtained from EQU. 2 at two closely spaced points (e.g., spaced by 0.001) to obtain a finite difference approximation to dphi3/dphi1.
<maths id="MATH-US-00006" num="00006"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mrow><mfrac><mo>∂</mo><mrow><mo>∂</mo><mi>ϕ1</mi></mrow></mfrac><mo></mo><mi>r2_d1</mi></mrow><mo>=</mo><mrow><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo></mo><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>arctan</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ3</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mi>%2</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ3</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mi>%2</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mrow></mfrac><mo>)</mo></mrow></mrow><mo>-</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mi>_switch</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%4</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%3</mi></mrow><mrow><mi>%1</mi><mo></mo><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mo></mo><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>1</mn><mn>2</mn></msup><mo></mo><msup><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>2</mn><mn>2</mn></msup></mrow></mfrac></mrow></msqrt></mrow></mfrac><mo>-</mo><mrow><mrow><mo>(</mo><mrow><mrow><mo>-</mo><mfrac><mrow><mi>r1_switch</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%4</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%3</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mi>phiD</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mrow><msup><mi>%1</mi><mn>2</mn></msup><mo></mo><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mfrac></mrow><mo>-</mo><mrow><mi>r1_switch</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%4</mi><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mi>%2</mi></mrow><mo>)</mo></mrow></mrow><mo></mo><mfrac><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>1</mn><mn>2</mn></msup><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow><mn>2</mn></msup></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msup><mn>2</mn><mn>2</mn></msup></mrow></mfrac></mrow></msqrt></mrow></mfrac></mrow><mo>)</mo></mrow><mrow><mi>%1</mi><mo></mo><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mfrac></mrow></mrow><mo>)</mo></mrow><mo>/</mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><msup><mi>r1_switch</mi><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msup><mi>%4</mi><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msup><mi>%3</mi><mn>2</mn></msup></mrow><mrow><msup><mi>%1</mi><mn>2</mn></msup><mo></mo><mi>r2_d1</mi><mo></mo><msup><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow></msqrt></mrow></mrow><mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mrow><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>arctan</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ3</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mi>%2</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ3</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mi>%2</mi></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mrow></mfrac><mo>)</mo></mrow></mrow><mo>-</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>r1_switch</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%4</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%3</mi></mrow><mrow><mi>%1</mi><mo></mo><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mo></mo><mi>r1_switch</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%4</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mrow><mi>%3</mi><mo>/</mo><mrow><mo>(</mo><mrow><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>%1</mi><mo></mo><msqrt><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><msup><mi>r1_switch</mi><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msup><mi>%4</mi><mn>2</mn></msup><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msup><mi>%3</mi><mn>2</mn></msup></mrow><mrow><msup><mi>%1</mi><mn>2</mn></msup><mo></mo><mi>r2_d1</mi><mo></mo><msup><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%1</mi><mo></mo><mstyle><mtext>:</mtext></mstyle><mo>=</mo><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mi>phiD</mi><mo>)</mo></mrow></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%2</mi><mo></mo><mstyle><mtext>:</mtext></mstyle></mrow><mo>=</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%3</mi><mo></mo><mstyle><mtext>:</mtext></mstyle></mrow><mo>=</mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mrow><mi>%</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>2</mn></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo></mo><mstyle><mtext /></mstyle><mo></mo><mrow><mrow><mi>%4</mi><mo></mo><mstyle><mtext>:</mtext></mstyle></mrow><mo>=</mo><mrow><mrow><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mi>phiD</mi><mo>)</mo></mrow></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>phi1_phiD</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>phi1_phiD</mi><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>DE</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>4</mn></mrow></mtd></mtr></mtable></math></maths><br /> where, n1, n2 phi1, phi3 are as defined above; <br /> r2_d1 is the polar radial coordinate of the redefined portion <b>2112</b> of the second lens surface <b>2104</b>; <br /> phiD is the constant draft angle of the portion <b>2108</b> of the first surface <b>2102</b>, measured in a clockwise direction from the Z-axis, so that practical draft angles will be negatively valued, e.g., −5 degrees; <br /> phi1_phiD is the value of phi1 at phiD on the first surface defined by DE1; <br /> r1_switch is the polar radial coordinate of the point on the first surface <b>2102</b> at which the switch is made to the constant draft portion <b>2108</b>, i.e., r1(phi1_phiD)=r1_switch. Although DE4 is defined in the domain of phi1, the polar angular coordinate phi2 of the redefined portion <b>2112</b> is given by:
<maths id="MATH-US-00007" num="00007"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>phi2_d1</mi><mo>=</mo><mrow><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mi>π</mi></mrow><mo>+</mo><mi>phiD</mi><mo>-</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mrow><mo>-</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>r1_switch</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mi>phiD</mi><mo>)</mo></mrow></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>phi1_phiD</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>phi1_phiD</mi><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow><mo></mo><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi><mo>+</mo><mrow><mi>arcsin</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ1</mi><mo>-</mo><mi>phiD</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow><mo>/</mo><mrow><mo>(</mo><mrow><mrow><mo>(</mo><mrow><mrow><mrow><mi>tan</mi><mo></mo><mrow><mo>(</mo><mi>phiD</mi><mo>)</mo></mrow></mrow><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow><mo></mo><mi>r2_d1</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>5</mn></mrow></mtd></mtr></mtable></math></maths><br /> Cartesian coordinate of the redefined portion can be obtained from r2_d1 and phi2_d1. <br /> In order to find the value of phi1 at which the inner lens surface has an angle equal to a desired draft the following equation is used:
<maths id="MATH-US-00008" num="00008"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>phiD</mi><mo>=</mo><mrow><mi>ϕ1</mi><mo>-</mo><mfrac><mi>π</mi><mn>2</mn></mfrac><mo>-</mo><mi>θ1</mi></mrow></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>6</mn></mrow></mtd></mtr></mtable></math></maths><br /> where theta<sub>—</sub>1 is the angle of incidence of ideal rays on the first surface and is given by:
<maths id="MATH-US-00009" num="00009"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>θ1</mi><mo>:=</mo><mrow><mo>-</mo><mrow><mi>arctan</mi><mo></mo><mrow><mo>(</mo><mfrac><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo></mo><mi>ϕ1</mi></mrow><mo>+</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mrow><mi>ϕ3</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mrow><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><mo></mo><mi>ϕ1</mi></mrow><mo>+</mo><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo></mo><mrow><mi>ϕ3</mi><mo></mo><mrow><mo>(</mo><mi>ϕ1</mi><mo>)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>7</mn></mrow></mtd></mtr></mtable></math></maths>
EQU. 6 (with theta<sub>—</sub>1 defined by EQU. 7) is used by plugging in a selected value for phiD (e.g., −½ to minus a few degrees) and using a root finding method to find the value of phi1 that balances EQU. 6. Table II below list information for the lens shown in <figref idrefs="DRAWINGS">FIG. 21</figref>
<tables id="TABLE-US-00002" num="00002"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="3"><colspec colname="1" colwidth="14pt" align="left" /><colspec colname="2" colwidth="91pt" align="left" /><colspec colname="3" colwidth="112pt" align="left" /><thead><row><entry namest="1" nameend="3" rowsep="1">TABLE II</entry></row><row><entry namest="1" nameend="3" align="center" rowsep="1" /></row></thead><tbody valign="top"><row><entry /><entry>Phi1_MIN</entry><entry>0.0 radians</entry></row><row><entry /><entry>Phi1_MAX</entry><entry>1.57 radians (90 degrees)</entry></row><row><entry /><entry>Phi3_MIN</entry><entry>0.0 radians</entry></row><row><entry /><entry>Phi3_MAX</entry><entry>1.57 radians (90 degrees)</entry></row><row><entry /><entry>PhiD</entry><entry>−0.087 radians (−5.0 degrees)</entry></row><row><entry /><entry>Phi1_phiD</entry><entry>1.13 radians (64.7 degrees)</entry></row><row><entry /><entry>rad_in(phi1)</entry><entry>Quasi Lambertian measured</entry></row><row><entry /><entry /><entry>data</entry></row><row><entry /><entry>rad_out(phi3)</entry><entry>1.0 (uniform goal)</entry></row><row><entry /><entry>r1_ini</entry><entry>3.0</entry></row><row><entry /><entry>r2_ini</entry><entry>4.0</entry></row><row><entry /><entry>n1</entry><entry>1.0</entry></row><row><entry /><entry>n2</entry><entry>1.497 (PMMA)</entry></row><row><entry /><entry>Phi_start</entry><entry>Phi1_min</entry></row><row><entry /><entry>Calculated Transmission</entry><entry>92.19%</entry></row><row><entry namest="1" nameend="3" align="center" rowsep="1" /></row></tbody></tgroup></table></tables>
Phi_start is the angle at which the initial conditions are specified.
Due to, at least, the finite size of LEDs and edge effects the lenses will not produce perfect fidelity to the intended light distribution (rad_out). One way to improve fidelity is to measure the actual distribution produced by the lenses and make successive prototypes where rad_out in the above equation is adjusted by subtracting a function of phi2 or phi3 (the output domain variable), that represents the error between the intended distribution rad_out and the actual measured data. Thus rad_out as it appears above, used to make an N<sup>TH </sup>prototype lens, would be replaced by:
<maths id="MATH-US-00010" num="00010"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mi>rad_out</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>p</mi></mrow><mo>)</mo></mrow></mrow><mo>-</mo><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo></mo><mrow><msub><mi>Error</mi><mi>i</mi></msub><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>p</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>8</mn></mrow></mtd></mtr></mtable></math></maths><br /> where φp stands for φ2 in the case of DE1 and φ3 in the case of DE2-DE4, and Error<sub>i </sub>is just the difference between the measured distribution and rad_out for an i<sup>TH </sup>prototype after both have been normalized to the same integrated power. Error<sub>i </sub>is conveniently represented as a cubic-spline. In establishing Error<sub>i </sub>measurements at positive and negative angles φ will be averaged together because rotational symmetry is assumed.
In making such corrections the error at the maximum value of φp (e.g., the error based on measurements at ±90° can be ignored by setting Error<sub>i</sub>(φp_max)=0.0. In this way, no attempt will be made to counteract the edge effect which will be accepted.
<figref idrefs="DRAWINGS">FIG. 22</figref> is a graph showing the radiant light intensity versus polar angle for an LED that produces a quasi-Lambertian light distribution as a series of measured data points along with a plot of the Lambertian distribution. In <figref idrefs="DRAWINGS">FIGS. 22-23</figref> the abscissa indicates polar angle in degrees and the ordinate indicates radiant light intensity in relative units. The Lambertian distribution which theoretically applies to a flat diffuse light emitter is simply cos(φ). The measured data is taken from a white XPC LED manufactured by Cree of Durham, N.C. As can be seen the distribution produced by the actual LED is nearly Lambertian and is termed ‘quasi-Lambertian’. Both were normalized to have an average of unity. The Standard Deviation of the measured distribution is 0.59 and the average absolute value deviation is 0.53. If bare LEDs producing such distribution were used in the omnidirectional LED light bulbs described herein the light distribution produced would be highly non-uniform. In the present context the average absolute value deviation is defined as the average of values measured at 5° intervals starting at a polar angle of −90° and ending at polar angle of 90°.
<figref idrefs="DRAWINGS">FIG. 23</figref> is a graph showing the radiant intensity versus polar angle for the XPC LED with two prototypes of a lens of the type shown in <figref idrefs="DRAWINGS">FIG. 21</figref> designed to produce a uniform light distribution. The first light distribution represent by the box-shaped points was for the first prototype with rad_out simply set to unity. The second distribution represent by the diamond-shaped points was for a second prototype with rad_out replaced given by EQU 8 with the error term based on measurements of the first prototype. Both light distributions were normalized to a mean value of unity as in the case of the quasi-Lambertian distribution shown in <figref idrefs="DRAWINGS">FIG. 22</figref>. The standard deviation for the first prototype is 0.210 and the standard deviation for the second prototype is 0.197. The respective average absolute value deviations are 0.104 and 0.0922. Significantly the central intensity maximum of the second prototype was reduced to 14% above average compared to 22% above average for the first prototype. The lines on the graph are at the 90% and 110% of average levels. Further improvement in uniformity may be obtainable with further prototypes defined using EQU. 8. In any case the uniformity is much improved compared to the distribution produced by the bare LED as shown in <figref idrefs="DRAWINGS">FIG. 22</figref>. The light distributions are sufficiently uniform that the enhancement in uniformity brought by using a diffusive bulb shaped cover is not needed in many cases and in certain embodiments the bulb shape cover need not be used. Generally it is preferable to have the average absolute value deviation of below 0.25 more preferably below 0.15 (measured with the data normalized to an average value of 1.0). The average absolute value deviation, as discussed herein, is computed using the following formula:
<maths id="MATH-US-00011" num="00011"><math overflow="scroll"><mtable><mtr><mtd><mrow><mi>AvgAbsDev</mi><mo>=</mo><mrow><mfrac><mn>1</mn><mn>37</mn></mfrac><mo></mo><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>37</mn></munderover><mo></mo><mrow><mi>abs</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>RadOutMeas</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mi>EQU</mi><mo>.</mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mn>9</mn></mrow></mtd></mtr></mtable></math></maths>
RadOutMeas<sub>i </sub>are 37 normalized measurements of light intensity taken at 5° spacing of polar angle φ from −90° to 90°. The measurements are normalized so that their average is equal to 1.0.
<figref idrefs="DRAWINGS">FIG. 24</figref> schematically illustrates a LED support/heat sink <b>2402</b> as described above in a coordinate system. This is useful in understanding how the LEDs equipped with the lenses described above will illuminate the full 4Pi Steradian solid angle about the bulbs in a highly uniform manner. Note that the Z-axis of the coordinate system is parallel to the longitudinal axis of the bulbs. Note also that the optical axis of the LEDs (axis of symmetry of the emission pattern of the LEDs) labeled N is perpendicular to the Z-axis.
<figref idrefs="DRAWINGS">FIG. 25</figref> shows an end view of an LED support/heatsink <b>2502</b> of the design described above. The cross-sectional shape is square meaning that it has 2-fold rotation symmetry (as well as fourfold) There are four LEDs <b>2504</b> shown (more may be used) on four faces <b>2506</b>. The faces <b>2506</b> are oriented 90 degrees apart in azimuthal angle θ (see <figref idrefs="DRAWINGS">FIG. 24</figref>), e.g., at 0°, 90°, 180°, 270°. Each LED is equipped with a lens of the type shown in <figref idrefs="DRAWINGS">FIG. 20</figref> or <figref idrefs="DRAWINGS">FIG. 21</figref> and described by DE1 or DE2-DE4, so that each LED illuminates a full hemisphere of 2π Steradian with a light distribution that is relatively uniform, i.e. a light distribution that has an average absolute value deviation below 0.25 and more preferably below 0.15. The arrangement of LEDs can be described as including two pairs with each pair including two LEDs that face in opposite direction. Thus, each pair including two LEDs that face in opposite directions will illuminate the full 4π Steradian solid angle around the bulb and the two pairs together will cover the full 4π Steradian solid angle twice over. In this case, only in a very small polar angle range (in the bulb coordinate system shown in <figref idrefs="DRAWINGS">FIG. 24</figref>) will the low intensity in the small (<5°) interval near phi=90° shown in <figref idrefs="DRAWINGS">FIG. 23</figref> not be mitigated by being combined with higher intensity light from an LED on another face <b>2506</b>. Other LED support/heat sinks that have 2n-fold symmetry where n is an integer can also provide redundant coverage of the full 4π Steradian solid angle while still providing a high degree of azimuthal uniformity.
While the invention has been described above with reference to particular embodiments shown in the figures and described above, the invention should not be construed as limited by these particular embodiments.
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| Notice of Allowance Data Verification CompletedAllowedN/=. | N/=. | |
| Reasons for AllowanceEX.R | EX.R | |
| Date Forwarded to ExaminerFWDX | FWDX | |
| Substitute Specification FiledC604 | C604 | |
| Response after Non-Final ActionA... | A... | |
| Request for Extension of Time - GrantedXT/G | XT/G | |
| Mail Non-Final RejectionNon-final rejectionMCTNF | MCTNF | |
| Non-Final RejectionNon-final rejectionCTNF | CTNF | |
| Interview Summary - Examiner InitiatedEXIE | EXIE | |
| Date Forwarded to ExaminerFWDX | FWDX | |
| Disposal for a RCE / CPA / R129AbandonedABN9 | ABN9 | |
| Application Return from OIPEWROIPE | WROIPE | |
| Applicant Has Filed a Verified Statement of Micro Entity Status in Compliance with 37 CFR 1.29MICR | MICR | |
| Applicant Has Filed a Verified Statement of Small Entity Status in Compliance with 37 CFR 1.27SMAL | SMAL | |
| Application Return TO OIPEROIPE | ROIPE | |
| Information Disclosure Statement consideredIDSC | IDSC | |
| Letter Requesting Interview with ExaminerM865 | M865 | |
| Request for Continued Examination (RCE)RCEX | RCEX | |
| Request for Extension of Time - GrantedXT/G | XT/G | |
| Information Disclosure Statement (IDS) FiledWIDS | WIDS | |
| Workflow - Request for RCE - BeginBRCE | BRCE | |
| Mail Final Rejection (PTOL - 326)Final rejectionMCTFR | MCTFR | |
| Final RejectionFinal rejectionCTFR | CTFR | |
| Information Disclosure Statement consideredIDSC | IDSC | |
| Electronic Information Disclosure StatementEIDS. | EIDS. | |
| Information Disclosure Statement (IDS) FiledWIDS | WIDS | |
| Date Forwarded to ExaminerFWDX | FWDX | |
| Response after Non-Final ActionA... | A... | |
| Request for Extension of Time - GrantedXT/G | XT/G | |
| Mail Non-Final RejectionNon-final rejectionMCTNF | MCTNF | |
| Non-Final RejectionNon-final rejectionCTNF | CTNF | |
| Case Docketed to Examiner in GAUDOCK | DOCK | |
| Case Docketed to Examiner in GAUDOCK | DOCK | |
| PG-Pub Issue NotificationPG-ISSUE | PG-ISSUE | |
| Application Dispatched from OIPEOIPE | OIPE | |
| Information Disclosure Statement consideredIDSC | IDSC | |
| Electronic Information Disclosure StatementEIDS. | EIDS. | |
| Information Disclosure Statement (IDS) FiledWIDS | WIDS | |
| Sent to Classification ContractorPGPC | PGPC | |
| Filing ReceiptFLRCPT.O | FLRCPT.O | |
| Notice of DO/EO Acceptance MailedM903 | M903 | |
| 371 Completion Date371COMP | 371COMP | |
| Preliminary AmendmentA.PE | A.PE | |
| Additional Application Filing FeesADDFLFEE | ADDFLFEE | |
| Applicants have given acceptable permission for participating foreignAPPERMS | APPERMS | |
| A statement by one or more inventors satisfying the requirement under 35 USC 115, Oath of the ApplicOATHDECL | OATHDECL | |
| Notice of DO/EO Missing Requirements MailedM905 | M905 | |
| Request for Foreign Priority (Priority Papers May Be Included)RQPR | RQPR | |
| Copy of the International ApplicationCPYIA | CPYIA | |
| Cleared by OIPE CSRL194 | L194 | |
| Initial Exam Team nnIEXX | IEXX |
6 legal events, as the office reported them to INPADOC
Over the term
Point at a mark for the eventEvents
| Event | Code | |
|---|---|---|
| Lapsed due to failure to pay maintenance feeLapsedFP | FP | |
| Lapse for failure to pay maintenance feesLapsedPATENT EXPIRED FOR FAILURE TO PAY MAINTENANCE FEES (ORIGINAL EVENT CODE: EXP.); ENTITY STATUS OF PATENT OWNER: MICROENTITYLAPS | LAPS | |
| Information on status: patent discontinuationPATENT EXPIRED DUE TO NONPAYMENT OF MAINTENANCE FEES UNDER 37 CFR 1.362STCH | STCH | |
| Fee payment procedureMAINTENANCE FEE REMINDER MAILED (ORIGINAL EVENT CODE: REM.); ENTITY STATUS OF PATENT OWNER: MICROENTITYFEPP | FEPP | |
| Fee paymentFPAY | FPAY | |
| Information on status: patent grantGrantedPATENTED CASESTCF | STCF |
Numbers
- Publication
- 08680754
- Publication, DOCDB
- 8680754
- Publication, EPODOC
- US8680754
- Application
- 12746800
- Application, DOCDB
- 74680009
- Application, EPODOC
- US20090746800
Titles
- English
- Omnidirectional LED light bulb
Patent term adjustment
- A delay
- +121 daysthe office missed an examination deadline
- Applicant delay
- −316 days
- Net adjustment
- 0 days
Classification
- CPC, 16
- F21V29/63
- F21K9/232
- F21V3/02
- F21V29/506
- F21V29/677
- F21V29/745
- F21V29/75
- F21V29/76
- F21V29/763
- F21V29/77
- F21V29/80
- F21Y2107/30
- F21Y2115/10
- F21K9/64
- G02B19/0019
- G02B19/0061
- IPC, 2
- F21V3 02
- F21V5 04
- USPC, 3
- 313046000
- 362235000
- 362294000